Comment #11 on issue 1878 by [email protected]: For non-commutative symbols all comparisons evaluate to False
http://code.google.com/p/sympy/issues/detail?id=1878

Actually, the way things are now might be confusing but it's consistent:

In [1]: a,b = symbols("a b", commutative=False)

In [2]: a - b > 0
Out[2]: 0 < a - b

In [3]: (a - b).is_positive
Out[3]: False

So, "is_positive" means "is real and greater than 0", while "> 0" means just that and
does not imply real.

I think now that it's probably best to leave things as they are.

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